Terms & Definitions

A cryptographically strong random number generator passes all statistical tests that run in polynomial time asymptotically. It will pass any statistical test for randomness that does not require an exponentially increasing to infinite amount of time to run. All such polynomial time statistical tests will be unable to distinguish the random number generator from a true random source.

The values produced by the generator are random in an absolutely precise way. There is absolutely no better way to predict the sequence than by tossing a coin. Furthermore, having a large chunk of output from the random number generator does not help in predicting past or future values.